Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 8th Semester (Eight Semester) 2014-15 EME 051 Operations Research Question Paper
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(Following Paper ID and Roll No. to be ?lled in your Answer Book)
PAPER ID : 140851
Roll No.
B. Tech.
(SEM. VIII.) THEORY EXAMLNAHON, 2014-15
OPERATION S RESEARCH
Time : 3 Hours] | [Total Marks ; 100
Note : Attempt all the questions. Assume missing data suitably.
Attempt any two of the following questions? I 10x2=20
1 (a) What is meant by a mathematical model of a real
situation? Discuss the importance of models in the
solution of OR problems.
(b) Use the graphical method to solve the following
LP problem :
MaximizeZ = 3x1 + 4x2
Subject to the constraints
(1) x1 - x2 = -1
(ii) ?x1 + x2 5 0 and x1, x2 3 0.
140851] 1 [ Contd...
(c) Solve the following'LP problem by using the two-
phase simplex method
Minimize Z = x1 - 2x26 - 3x3
Subject to the constraints :
(1) ?2x1 + x2 + 3X3 = 2
(2) 2x1+ 3x2 + 4x3 = 1 and x1, x2, x3 2 0'
Attempt any two of the following questions : 10x2=20
2 (a) A manufacturer wants to ship 22 loads of his
140851]
products as shown below! The matrix gives the
kilometers from sources of supply to the
destinations.
Dl D2 D3 D4 D5 Supply
S1 5 8 6 6? 3 8
55 4 7 7 6 5 5
S3 8 4 6 6 4 9
Demand 4 4 5 4 8 22
2 5
The shipping cost is Rs. 10 per load per km.
What shipping schedule should be used in order
to minimize the total transportation cost?
2 | CO'Itd...
(b)
(C)
A Marketing manager has ?ve salesman and ?ve
sales districts. Censidering the capabilities of the
salesman and the nature of the districts, the
marketing manager estimates that the sales per
month (in hundred; rupees) for each salesman in
. each district would be as follows:
Districts ?
At SB (1 I) :E
1 32 38 40 28 40
Salesman 2 40 24 28 21 36
3 41 27 33 -30 37
4 22 38 41 36' 36
5 29 33 40 35 39
F ind the assignment of salesman to district that
will remain in maximum sales. .
State Bellman's "principle of optimality" and explain
with the help of an illustrative example how it can
be used to solve a multistage decision problem,
Attempt any two of the following questions :
3 (3)
140851]
le2= 20
An investor is given the following investment
alternatives and percentage rates of return.
States of Nature ( Market Conditions)
Low Medium High
Regular shares 7% 10% 15%
Risky shares -10% 12% 25%
Property - l 2% 1 8% 30%
3 [V Contd...
Over the past 300. days; 150 days have been
medium market conditions and 60 days have had
high market increases. On the basis of these data,
state the optimum investment strategy for the
investment.
(b) For what value of X, the game with following pay-
o?? matrix is strictly determinable?
Player A Player B
B1 B2 B3
A, A 6 2
A2 -1 x ~7
A3 -.2 4 7L
(c) There are Seven jobs, each of which has to go
through the machines A and B in the order AB.
Processing times in hours are as follows:
qr
Job 1 2 3 4 5 6 7
MachineA 3 12 15 6 10 11 9
MachineB 8 10 10, 6 12 1 3
Determine a sequence of these jobs that will
minimize the total elapsed time T. Also ?nd T and
idle time for machine A and B.
140851] 4 [_ Contd...
Attempt any two of the following questions : 10x2=20
4 (a) The demand for an item in a company is
18,000 units per year, and the company
can produce the item at a rate of 3,000 K/
per month. The. cost of one. set up is Rs 500
and the holding cost of one unit per month is 15
paise. The shortage cost of one unit is Rs 240
per year. Determine the optimum manufacturing
quantity and the number of shortages. Also
determine the manufacturing time and the time
between set-ups.
(b) What is Monte Carlo simulation? Describe the
idea of experimentation (Random Sampling) in
simulation.
(0) Using random numbers to simulate a sample, ?nd
the probability that a packet of 6 products does
not contain any defective product, when the
production line produces 10 percent defective
products. Compare the answer with the expected
probability.
140851] 5 |? Contd...
Attempt any two of the following questions :
10x2=20
5 (a) Explain the following terms in PERT/CPM.
(1) Earliest time
(1i) Latest time
(1h) Total activity time
(1v) Event slack
(v). Critical path.
(b) The following tasks has to be performed periodically
on the heat exchangers in a re?nery:
Task _ Innnediate predecessors Time (days)
A - 14
B A 22
C B '10
D B 16
E B 12
F C 1 0
G C 6
H F ,G 8
I [xElI 24
J I 16
(1) Draw a network diagram of activities for
the project.
(1i) Identify the critical path. What is its length?
140851] 6
[ Contd...
(c) In a railway marshalling yard, goods trains arrive
at a rate of 30 trains per day. Assuming that the
inter am'val time follows an exponential distribution
and the service time (the time taken to hump a
train) distribution is also exponential with an
average of 36 minutes. Calculate:
(1) expected queue size (line length)
(1i) Probability that the queue size exceeds 10.
If the input of trains increases to an average
of 33 per day, What will be the change in
(a) and (b) ?
140851] 7 I 3575]
This post was last modified on 29 January 2020